Video poker variance:
the part RTP
leaves out.
Variance measures how widely payouts spread around their average. Higher variance means bigger swings at the same stake, not a higher return.
Two games can return almost the same over the long run and feel very different over 1,000 hands. The missing detail is how much of that return rests on rare, large payouts.
Return tells you the average.
Variance tells you about the spread.
“Volatility” is the everyday word for the swings. Variance is a precise measure of them, and standard deviation puts that measure back into units you can use.
99.54%
With the best play on 9/6 Jacks or Better, every $100 bet pays back $99.54 on average. That isn’t a promise about a $100 deposit or about any one session.
19.51
Each payout’s squared distance from the average, weighted by its chance. It’s measured in bets squared, so it compares how much games swing at the same stake.
4.42 bets
The square root of 19.51: the spread of one hand, in bets. It is not an expected loss, a maximum loss or a bankroll.
9/6 Double Double Bonus has about 2.15× the variance of 9/6 Jacks or Better, but 1.47× the standard deviation. “Twice the variance” doesn’t mean dollar swings twice the size.
Compare the whole game,
not just the jackpot.
Of these full-royal pay tables, Jacks or Better has the lowest variance and 9/7 Triple Double Bonus the highest, 5.04 times as much as 9/6 Jacks or Better. Check the return next to the variance: a smoother game can still be worse value.
Eight of the 21 pay tables · each played the best way
The dollar SD is for 1,000 hands on fresh deals at $1.25 a hand. Pick a game to explore its sessions.
| Game and pay table | Return | Variance | Dollar SD over 1,000 hands |
|---|---|---|---|
| 9/6 Jacks or Better, under five credits Royal pays 250 for 1 | 98.3735% | 4.93 | $87.74 |
| 6/5 Jacks or Better | 94.9961% | 19.04 | $172.50 |
| 7/5 Jacks or Better | 96.1472% | 19.17 | $173.08 |
| 8/5 Jacks or Better | 97.2984% | 19.32 | $173.76 |
| 8/6 Jacks or Better | 98.3927% | 19.34 | $173.84 |
| 9/5 Jacks or Better | 98.4498% | 19.50 | $174.53 |
| 9/6 Jacks or Better | 99.5439% | 19.51 | $174.62 |
| 7/5 Bonus Poker | 98.0147% | 20.75 | $180.08 |
| 8/5 Bonus Poker | 99.1660% | 20.90 | $180.73 |
| Illinois Deuces Wild | 98.9131% | 25.62 | $200.07 |
| 17/7/5 Joker Poker | 98.0854% | 25.65 | $200.21 |
| Not So Ugly Ducks Deuces Wild | 99.7283% | 25.78 | $200.70 |
| Full-pay Deuces Wild | 100.7620% | 25.83 | $200.91 |
| 20/7/5 Joker Poker | 100.6463% | 26.25 | $202.50 |
| 10/7 Double Bonus Straight pays 5 for 1 | 100.1725% | 28.26 | $210.12 |
| 9/6 Double Bonus | 97.8062% | 30.78 | $219.30 |
| 9/6 Bonus Poker Deluxe | 99.6417% | 32.13 | $224.07 |
| 9/6 Double Double Bonus | 98.9808% | 41.98 | $256.13 |
| 8/5 Double Double Bonus | 96.7861% | 41.99 | $256.16 |
| 10/6 Double Double Bonus | 100.0670% | 42.18 | $256.71 |
| 9/7 Triple Double Bonus | 99.5778% | 98.28 | $391.87 |
The exact pay table matters.
“9/6” names what the full house and the flush pay. Double Bonus, wild-card games and kicker bonuses need more than that. The payout breakdown below shows every award, the royal included, for all 21 tables.
Above 100% is still an average.
Full-pay Deuces Wild returns 100.76% with the best play, yet 63.80% of its 1,000-hand sessions finish behind. An edge on paper doesn’t guarantee a win, or that you’ll find that table where you play.
Lower variance isn’t automatically better. Cut the 9/6 Jacks or Better royal from 800 to 250 for 1 and the variance falls from 19.51 to 4.93, but the return with the best play falls too, from 99.54% to 98.37%. If you need a smaller stake, check whether a lower credit value keeps the full royal.
The average is only
one part of the story.
Choose a pay table, a stake and a number of hands. See the average next to the middle result and the chance of actually finishing ahead.
Enter the whole hand’s bet: five 25¢ credits make $1.25. One hand at a time, the same stake throughout.
9/6 Jacks or Better · 1,000 hands · $1.25 a hand
Every result averaged together, rare jackpots included.
At least half of sessions finish at or below this.
The median sits $25.55 below the average. A few big wins pull the average up.
Where sessions finish
- Behind
- 64.87%
- Break even
- 0.56%
- Ahead
- 34.57%
A bigger or smaller stake scales the dollars. It doesn’t change these chances while the pay table and the strategy stay the same.
A range from the actual payouts
5th to 95th percentile- 5th percentile
- −$150.00
- Median
- −$31.25
- 95th percentile
- +$125.00
About 90% of sessions end between the two cut-offs, sometimes a little more because results land on exact amounts. They aren’t the lowest or highest results: sessions can end outside them.
- Total amount bet
- $1,250.00
- Session standard deviation
- $174.62
- Chance of at least one royal
- 2.45%
Standard deviation measures the spread around the average. It isn’t a loss limit or a bankroll, and it isn’t a range that holds 68% of video poker sessions.
What this assumes
The best play for this exact pay table, a fresh deal every hand, and enough money to finish every hand. The royal pays 800 for 1.
Stopping early, running out of money and playing several hands from one deal are not included.
How it’s worked out
Let x be what a hand pays for each unit bet and p its chance. The average payout is μ = Σpx and the variance is v = Σp(x − μ)². Taking off the stake moves the average, not the variance.
Expected net resultN × b × (μ − 1)
Session standard deviationb × √(N × v)
N is the number of hands, each on a fresh deal, and b the whole stake a hand: five 25¢ credits make b = $1.25. One payout’s share of the variance is p(x − μ)² ÷ v.
The chances and percentiles come from combining the payouts of every hand in the session (with a fast Fourier transform), not from simulated sessions. Rounding and vanishingly rare results aside, they are exact. Where two holds are worth exactly the same, the one keeping more cards counts; another choice can move a hand’s frequency slightly without changing the return.
A tiny chance.
An outsized effect.
The royal is rare, but its payout is a long way from the average, and variance squares that distance. That’s how a hand you almost never see can carry most of a game’s swings.
The session explorer above follows the game you pick here.
9/6 Jacks or Better · the best play · the royal pays 800 for 1
On this table, the royal is 80.99% of the variance. The most common result, no payout, is only 2.77%.
See the whole pay table, how often each hand comes and its share of the variance
| Final hand | Pays for 1 | How often | Share of the variance |
|---|---|---|---|
| Royal flush | 800 | 1 in 40,391 | 80.99% |
| Straight flush | 50 | 1 in 9,148 | 1.35% |
| Four of a kind | 25 | 1 in 423 | 6.98% |
| Full house | 9 | 1 in 86.9 | 3.78% |
| Flush | 6 | 1 in 90.8 | 1.41% |
| Straight | 4 | 1 in 89.1 | 0.52% |
| Three of a kind | 3 | 1 in 13.4 | 1.53% |
| Two pair | 2 | 1 in 7.7 | 0.67% |
| Pair of jacks, queens, kings or aces | 1 | 1 in 4.7 | <0.01% |
| No payout | 0 | 1 in 1.8 | 2.77% |
| The whole game | 99.5439% return | Every hand | 100% |
The source of the swing can change.
In 9/7 Triple Double Bonus, four aces with a 2, 3 or 4 pay 800 for 1 and make up 45.70% of the variance. The royal adds only 14.32%. It’s the whole list of payouts, not the royal alone, that sets the swings.
A royal cycle is not a deadline.
The royal cycle on 9/6 Jacks or Better is 40,391 hands, an average. Even after that many fresh hands, 36.79% of runs have no royal. After a long dry spell, the next fresh deal has the same chance as ever: a long wait doesn’t make a jackpot due.
The stake changes the dollars.
The bankroll decides whether you can carry on.
To shrink the swings, start with the stake.
Same pay table, same number of hands: cut the stake from $1.25 to $0.25 and every dollar figure, the standard deviation included, falls to a fifth. The game’s variance in bets stays the same.
$1.25 a hand$174.62
$0.25 a hand$34.92
Fewer hands bring the total bet down too. At the same stake, a quarter of the hands halves the dollar standard deviation and quarters the expected loss. Neither changes the house edge on each dollar bet.
Why “the 5th percentile is −$150” doesn’t mean “bring $150”.
The explorer shows where a finished session ends, and it assumes every hand can be paid for. A bankroll asks something else: whether you run out before you get there.
A session can dip below where it finishes and then recover, but only if there’s money left for the next hand. Bring exactly $150.00 to 1,000 hands of 9/6 Jacks or Better at $1.25 and you run out in 8.10% of sessions, not 5%. Finishing 19 sessions in 20 takes $165.00.
Set a loss limit you can afford first. If a game’s swings don’t fit it, a smaller stake or a shorter session will. Adding money to chase the average doesn’t improve the odds.
Playing several hands from one deal? They share their first five cards, so their results move together, and the session figures above can’t treat 100 lines as 100 fresh deals. Compare multi-hand stakes and swings
What variance can tell you.
And what it can’t.
Which video poker game has the lowest variance?
Of the full-royal pay tables here, Jacks or Better has the lowest: 19.51 for 9/6, against 20.90 for 8/5 Bonus Poker and 41.98 for 9/6 Double Double Bonus. That doesn’t hold for every video poker game there is. A smaller royal brings the variance down much further, and the return with it, so compare the exact pay table, the strategy and the stake.
Is variance the same as volatility?
Volatility is the everyday word for how much results swing, and variance is one way to measure it. Labels like “low”, “medium” or “high” have no agreed cut-offs. A quoted variance tells you more, as long as you know the pay table and that it’s measured in whole bets.
Why can I lose much more than the house edge suggests?
The house edge is an average over every possible result, rare jackpots included, and your session may not include them. On 9/6 Jacks or Better, 1,000 hands at $1.25 average −$5.70, but the median is −$31.25, and single sessions land far to either side. The total bet also counts winnings you play again, so it can be many times the money you started with.
Does one standard deviation contain about 68% of sessions?
That rule comes from the bell curve. Video poker sessions are lopsided, pulled by rare big payouts, so applying it without checking misleads. The explorer’s percentiles come from the game’s actual payouts for the session you pick; its standard deviation measures spread, not a range you can count on.
Does playing longer smooth out variance?
Your return on each dollar bet does settle down as you play more hands. But at the same stake, the spread of your total dollar result grows with the square root of the number of hands: four times the hands doubles the dollar standard deviation and, below 100% return, quadruples the expected loss. Playing on doesn’t force a losing session to recover.
Does betting five credits increase variance?
Two things change. A bigger total stake scales the dollar swings. And reaching the five-credit royal changes the payouts themselves: on 9/6 Jacks or Better the royal goes from 250 to 800 for 1, which raises the variance from 4.93 to 19.51 and the return from 98.37% to 99.54%. Compare the total amount at risk, and look at a lower credit value if it keeps the full royal at a stake you can afford.
Does a losing streak mean a game is due, or unfair?
A losing streak on its own shows neither. Wide swings fit a fair game, and fresh deals don’t remember what came before. Variance can’t tell you whether a particular casino’s game is fair; it only describes results under the stated cards, payouts and strategy.
Can good strategy get rid of variance?
No. The best strategy gets the highest average return out of a pay table, but random cards still make the payouts vary. Changing your holds to chase a royal, or to get paid more often, changes both the return and the spread, and the figures here no longer apply.
A small edge, a big swing.
Three things worth knowing before you sit down.
The same return can feel different
9/6 Jacks or Better and 9/7 Triple Double Bonus return 99.54% and 99.58%. Over 1,000 hands at $1.25, the middle result is −$31.25 on one and −$147.50 on the other.
The royal carries the swing
On 9/6 Jacks or Better the royal is 80.99% of the variance but only 1.99% of the money paid back, and just 2.45% of 1,000-hand sessions have one.
A loss cut-off is not a bankroll
The worst 1 in 20 sessions end at −$150.00 or worse. Bring exactly $150.00 and you run out in 8.10% of them; $165.00 finishes 19 in 20.